The 59-year-old Argentine coach will reportedly sign a contract with the Reds next week.
Calderon has worked in Saudi Arabian football teams Al-Ittihad and Al-Hilal.
He led Al-Ittihad to the 2009 AFC Champions League final, where the Saudi Arabian giant lost to Korean team Pohang Steelers 2-1.
Persepolis has negotiated with Ante Cacic, Massimo Carrera, Alexander Nouri, Krunoslav "Kruno" Jurcic, Walter Zenga and Takis Lemonis so far.
The new Persepolis coach will have a difficult task in the popular Iranian football club since Ivankovic led Persepolis to win the Iran Professional League title three times.
Under tutelage of the Croat, Persepolis also won a Hazfi Cup and three Super Cups.